Inference for??0 and ?1

1
Inference for??0 and ?1

• A few more comments

2
What if normality assumption violated?

• CIs and HTs for b0 and b1 depend on assumption
  that error terms (and hence observed yi for fixed
  xi) follow a normal distribution.
• Not a big deal if the error terms (and hence
  observed yi) are only approximately normal.
• If have a large sample, then the error terms can
  even deviate far from normality.

3
Interpretation of 95 confidence level

• If you conduct the same study a large number of
  times, say 100 times at the exact same (fixed)
  xi levels then youd expect 95 of your
  confidence intervals to contain the true value of
  the parameter you are estimating.

4
Spacing of X levels
The greater this quantity, the smaller Var(b0)
and Var(b1).
5
Errors are always possible!

• Dont forget that whenever you conduct a
  hypothesis test, you risk making a Type I error
  (reject null when it is true) or a Type II error
  (dont reject null when it is false).
• Minimize chance of making a Type I error by using
  small significance level (0.01, 0.05).
• Minimize chance of making a Type II error by
  having a large sample size.